517,453 research outputs found
Differential rotation of nonlinear r-modes
Differential rotation of r-modes is investigated within the nonlinear theory
up to second order in the mode amplitude in the case of a slowly-rotating,
Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the
linear r-mode, which represents differential rotation that produces large scale
drifts of fluid elements along stellar latitudes. This solution includes a
piece induced by first-order quantities and another one which is a pure
second-order effect. Since the latter is stratified on cylinders, it cannot
cancel differential rotation induced by first-order quantities, which is not
stratified on cylinders. It is shown that, unlikely the situation in the
linearized theory, r-modes do not preserve vorticity of fluid elements at
second-order. It is also shown that the physical angular momentum and energy of
the perturbation are, in general, different from the corresponding canonical
quantities.Comment: 9 pages, revtex4; section III revised, comments added in Introduction
and Conclusions, references updated; to appear in Phys. Rev.
Response of the common mode of interferometric detectors to a stochastic background of massive scalar radiation
We compute the angular pattern and the overlap reduction functions for the
geodesic and non-geodesic response of the common mode of two interferometers
interacting with a stochastic, massive scalar background. We also discuss the
possible overlap between common and differential modes. We find that the
cross-correlated response of two common modes to a non-relativistic background
may be higher than the response of two differential modes to the same
background.Comment: 8 pages, 4 figures, revte
Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell
Recent studies have raised doubts about the occurrence of r modes in
Newtonian stars with a large degree of differential rotation. To assess the
validity of this conjecture we have solved the eigenvalue problem for
Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the
presence of differential rotation. The results obtained indicate that the
eigenvalue problem is never singular and that, at least for the case of a
thin-shell, the analogues of r modes can be found for arbitrarily large degrees
of differential rotation. This work clarifies the puzzling results obtained in
calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ
Effects of Uniform and Differential Rotation on Stellar Pulsations
We have investigated the effects of uniform rotation and a specific model for
differential rotation on the pulsation frequencies of 10 \Msun\ stellar models.
Uniform rotation decreases the frequencies for all modes. Differential rotation
does not appear to have a significant effect on the frequencies, except for the
most extreme differentially rotating models. In all cases, the large and small
separations show the effects of rotation at lower velocities than do the
individual frequencies. Unfortunately, to a certain extent, differential
rotation mimics the effects o f more rapid rotation, and only the presence of
some specific observed frequencies with well identified modes will be able to
uniquely constrain the internal rotation of pulsating stars.Comment: 33 pages, 16 figures. Accepted for publication in Ap
Nonlinear modes of clarinet-like musical instruments
The concept of nonlinear modes is applied in order to analyze the behavior of
a model of woodwind reed instruments. Using a modal expansion of the impedance
of the instrument, and by projecting the equation for the acoustic pressure on
the normal modes of the air column, a system of second order ordinary
differential equations is obtained. The equations are coupled through the
nonlinear relation describing the volume flow of air through the reed channel
in response to the pressure difference across the reed. The system is treated
using an amplitude-phase formulation for nonlinear modes, where the frequency
and damping functions, as well as the invariant manifolds in the phase space,
are unknowns to be determined. The formulation gives, without explicit
integration of the underlying ordinary differential equation, access to the
transient, the limit cycle, its period and stability. The process is
illustrated for a model reduced to three normal modes of the air column
Pattern Formation by Boundary Forcing in Convectively Unstable, Oscillatory Media With and Without Differential Transport
Motivated by recent experiments and models of biological segmentation, we
analyze the exicitation of pattern-forming instabilities of convectively
unstable reaction-diffusion-advection (RDA) systems, occuring by means of
constant or periodic forcing at the upstream boundary. Such boundary-controlled
pattern selection is a generalization of the flow-distributed oscillation (FDO)
mechanism that can include Turing or differential flow instability (DIFI)
modes. Our goal is to clarify the relationships among these mechanisms in the
general case where there is differential flow as well as differential
diffusion. We do so by analyzing the dispersion relation for linear
perturbations and showing how its solutions are affected by differential
transport. We find a close relationship between DIFI and FDO, while the Turing
mechanism gives rise to a distinct set of unstable modes. Finally, we
illustrate the relevance of the dispersion relations using nonlinear
simulations and we discuss the experimental implications of our results.Comment: Revised version with added content (new section and figures added),
changes to wording and organizatio
Characterization of a Differential Radio-Frequency Single-Electron Transistor
We have fabricated and characterized a new type of electrometer that couples
two parallel single-electron transistors (SETs) to a radio-frequency tank
circuit for use as a differential RF-SET. We demonstrate operation of this
device in summing, differential, and single-SET operation modes, and use it to
measure a Coulomb staircase from a differential single Cooper-pair box. In
differential mode, the device is sensitive to uncorrelated input signals while
screening out correlated ones.Comment: 3 pages, 3 figures, submitted to Applied Physics Letter
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